English

The Beta-Bound: Drift constraints for Gated Quantum Probabilities

History and Philosophy of Physics 2026-02-02 v1 Quantum Physics

Abstract

Quantum mechanics provides extraordinarily accurate probabilistic predictions, yet the framework remains silent on what distinguishes quantum systems from definite measurement outcomes. This paper develops a measurement-theoretic framework for projective gating. The central object is the β\beta-bound, an inequality that controls how much probability assignments can drift when gating and measurement fail to commute. For a density operator ρ\rho, projector FF, and effect EE, with gate-passage probability s=Tr(ρF)s = {\rm Tr}(\rho F) and commutator norm ε=[F,E]\varepsilon = \|[F, E]\|, the symmetric partial-gating drift satisfies ΔpF(E)2(1s)/sε|\Delta p_F(E)| \leq 2 \sqrt{(1 - s)/s} \cdot \varepsilon. The constant 2 is sharp. We introduce two diagnostic quantities: the coherence witness W(ρ,F)=Fρ(IF)1W(\rho, F) = \|F \rho (I - F)\|_1, measuring cross-boundary coherence, and the record fidelity gap ΔT(ρF,R)\Delta_T(\rho_F, R), measuring expectation-value change under symmetrisation. Three experimental vignettes demonstrate falsifiability: Hong--Ou--Mandel interferometry, atomic energy-basis dephasing, and decoherence-induced classicality. The framework is operational and interpretation-neutral, compatible with Everettian, Bohmian, QBist, and collapse approaches. It provides quantitative structure that any interpretation must accommodate, along with a template for experimental tests.

Keywords

Cite

@article{arxiv.2601.22188,
  title  = {The Beta-Bound: Drift constraints for Gated Quantum Probabilities},
  author = {Jonathon Sendall},
  journal= {arXiv preprint arXiv:2601.22188},
  year   = {2026}
}

Comments

18 pages

R2 v1 2026-07-01T09:26:30.782Z